We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or f...

We consider di usion processes on a class of R{trees. The processes are de ned in a manner similar to that of Le Gall's Brownian snake. Each point in the tree has a real{valued \height" or \generation", and the height of the di usion process evolves as a Brownian motion. When the height process decreases the di usion retreats back along a lineage, whereas when the height process increases the d...

We develop a new framework to calibrate stochastic volatility option pricing models to an arbitrary prescribed set of prices of liquidly traded options. Our approach produces an arbitrage-free stochastic volatility di usion process that minimizes the distance to a prior di usion model. We use the notion of relative entropy (also known under the name of Kullback-Leibler distance) to quantify the...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

Synopsis We describe a model-free method to quantify the spectrum of water mobilities in ៯�xed and live brain tissues. We eliminate confounds caused by anisotropic di៛�usion in brain tissues by measuring orientationally-averaged di៛�usion weighted images over a large range of b-values. Spectra of orientationally-averaged water di៛�usivities show clear distinctions between white matter, gray mat...

We investigate the empirical performance of high-dimensional a¢ ne stochastic volatility and jump di¤usion (AJD) pricing models to …t S&P 500 stock index option prices.We use these models to study how to structure two kind of risk components: volatility factor and jump di¤usion within a multi-factor framework. We identify that more than two volatility factors are needed to be included into mode...

The completion of interrupted lines or the enhancement of ow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diiusion lter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with ...

We have measured the radon di!usion, solubility and permeability coe$cients of various foils being of interest for the Borexino experiment. The applied methods and instrumentation are described and the mathematical model for di!usion of Rn, including its decay, is outlined. A very strong in#uence of water on the Rn di!usion through nylon foils was found. The rather low Rn permeability for dry n...

The paper deals with the analysis of pair di usion models in semiconductor technology. The underlying model contains reaction-drift-di usion equations for the mobile point defects and dopant-defect pairs as well as reaction equations for immobile dopants which are coupled with a nonlinear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an exis...

That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of jump-di®usion models of the short rate to capture surprise e®ects, and show that these models o®er a good statistical distribution of short rate behavior, and are useful in understanding many empirical phenomena. Continuous-time and discrete-time estimators...